How to calculate the deflection of a wave washer?

Hey there! As a wave washer supplier, I often get asked about how to calculate the deflection of a wave washer. It's a crucial topic, especially for those who rely on these washers in their projects. So, let's dive right in and break it down.

What is a Wave Washer?

First things first, let's quickly go over what a wave washer is. A wave washer is a type of spring washer that has a wavy shape. This design allows it to provide a certain amount of spring force when compressed. Wave washers come in different materials, like stainless steel, and various configurations, such as the Stainless Steel Wave Washer and the Three Wave Washer. They're used in a wide range of applications, from automotive to electronics, to provide preload, absorb vibration, and compensate for thermal expansion.

Why Calculate the Deflection?

Calculating the deflection of a wave washer is important for several reasons. First, it helps you determine how much the washer will compress under a given load. This is crucial for ensuring that the washer functions as intended in your application. If the deflection is too high, the washer might not provide enough spring force. On the other hand, if the deflection is too low, the washer might not be able to absorb the required amount of vibration or compensate for expansion.

Factors Affecting Wave Washer Deflection

Before we get into the actual calculation, let's take a look at the factors that affect the deflection of a wave washer:

1. Material Properties: The type of material used for the wave washer plays a significant role in its deflection. Different materials have different elastic moduli, which determine how much the material can stretch or compress under a load. For example, stainless steel has a different elastic modulus compared to other metals, which will affect the deflection of a Stainless Steel Wave Washer.
2. Washer Dimensions: The dimensions of the wave washer, such as its outer diameter, inner diameter, thickness, and the number of waves, also affect its deflection. A larger outer diameter or a greater number of waves can result in a different deflection compared to a smaller one.
3. Load Applied: The amount of load applied to the wave washer is perhaps the most obvious factor affecting its deflection. The higher the load, the greater the deflection will be, within the elastic limit of the material.

The Calculation Process

Now, let's get to the nitty - gritty of calculating the deflection of a wave washer. There are a few different methods, but one of the most common ways is to use the following general formula:

$$\delta=\frac{8P(D_{o}^4 - D_{i}^4)}{E\pi n t^3}$$

Where:

• $\delta$ is the deflection of the wave washer
• $P$ is the load applied to the washer
• $D_{o}$ is the outer diameter of the washer
• $D_{i}$ is the inner diameter of the washer
• $E$ is the elastic modulus of the material used for the washer
• $n$ is the number of waves in the washer
• $t$ is the thickness of the washer

Let's break this down a bit further. The elastic modulus $E$ is a property of the material. For example, for stainless steel, the elastic modulus is typically around $190 - 210$ GPa. You can find the specific value for the material you're using from material property tables.

The outer and inner diameters, $D_{o}$ and $D_{i}$, are measured directly from the wave washer. Make sure to measure them accurately, as even a small error can lead to significant differences in the calculated deflection.

The number of waves $n$ is simply the count of the waves on the washer. And the thickness $t$ is the thickness of the material from which the washer is made.

Example Calculation

Let's say we have a Wave Spring Washer made of stainless steel with the following properties:

• Outer diameter $D_{o}= 20$ mm
• Inner diameter $D_{i}= 10$ mm
• Thickness $t = 1$ mm
• Number of waves $n = 3$
• Elastic modulus $E = 200$ GPa (or $200\times10^{3}$ MPa)
• Load applied $P = 50$ N

First, we need to convert all the units to the same system. Let's use millimeters and Newtons.

We calculate $(D_{o}^4 - D_{i}^4)=(20^4 - 10^4)=(160000 - 10000)=150000$ $mm^4$

Now, we substitute the values into the formula:

$$\delta=\frac{8\times50\times150000}{200\times10^{3}\times\pi\times3\times1^3}$$

$$\delta=\frac{6000000}{1884955.59}$$

$$\delta\approx 3.18$$ mm

So, under a load of 50 N, this wave spring washer will deflect approximately 3.18 mm.

Limitations of the Calculation

It's important to note that this formula is a simplified model. In real - world applications, there are other factors that can affect the deflection, such as manufacturing tolerances, surface finish, and the way the load is applied. Also, if the load exceeds the elastic limit of the material, the washer will undergo plastic deformation, and the formula will no longer be valid.

Using Software for Calculation

If you're dealing with complex wave washer designs or need more accurate results, you can use specialized engineering software. These programs take into account many more factors than the simple formula we used above. They can simulate the behavior of the wave washer under different loads and conditions, giving you a more accurate prediction of the deflection.

Conclusion

Calculating the deflection of a wave washer is an important step in ensuring its proper function in your application. By understanding the factors that affect deflection and using the appropriate calculation methods, you can select the right wave washer for your needs.

If you're in the market for high - quality wave washers, whether it's a Stainless Steel Wave Washer, a Three Wave Washer, or a Wave Spring Washer, I'm here to help. We offer a wide range of wave washers to meet your specific requirements. If you have any questions or want to discuss your procurement needs, feel free to reach out. We're always happy to have a chat and find the best solution for you.

References

• Shigley, J. E., & Mischke, C. R. (2001). Mechanical Engineering Design. McGraw - Hill.
• Budynas, R. G., & Nisbett, J. K. (2011). Shigley's Mechanical Engineering Design. McGraw - Hill.